math course sequence for physics

College Majors Science Majors
1

I posted this thread in the math section a while back, I thought I’d ask here to get some more opinions on it.

hi im a physics major and after calc 2 I can take intro to linear algebra and calc 3 in any order i wish before taking differential equations. which order would be best?

I was considering taking Calc III and Intro to Linear Algebra at the same time in the summer before I take Electricity & Magnetism. Then I planned on taking E&M at the same time as Intro to Differential Equations, and then take Optics/Modern Physics. Is taking Calc III and Intro to Linear Algebra at the same time during the summer(shorter time) too difficult? Will the content overlap… will I be missing knowledge based on the order of the things that are taught in CalcIII/Linear that overlap? Or should I just take Calc III in the summer, then Intro to Linear Algebra in the fall alongside E&M, and then Differential Equations alongside Optics/Modern Physics?

here are the catalog course descriptions:

Introduction to Linear Algebra This course serves as an introduction to the theory and applications of elementary linear algebra, and is the basis for most upper division courses in mathematics. The topics covered in this course include matrix algebra, Gaussian Elimination, systems of equations, determinants, Euclidean and general vector spaces, linear transformations, orthogonality and inner product spaces, bases of vector spaces, the Change of Basis Theorem, eigenvalues, eigenvectors, the rank and nullity of matrices and introduction to linear transformations.

Calculus with Analytic Geometry III This course includes the algebra and geometry of 2 and 3 dimensional Euclidean vectors, the algebra and calculus of multivariable functions including composition of functions, limits, continuity, partial differentiation, gradients, higher order derivatives, the chain rule, constrained and unconstrained optimization including Lagrange’s theorem, multiple integrals, integrals over paths and surfaces, and integral theorems of vector analysis. This course is intended as a general introduction to the theory and applications of multivariable calculus. This course is essential for most upper division courses in mathematics and forms part of the foundation for engineering and physics.

thanks for the help!

2

Linear Algebra is most important when you take quantum mechanics which will not be until yourJunior or Senior year. Multivariate Calculus & Differential Equations are absolutely necessary by the time you take your Junior year Classical Mechanics course(s) (not the beginning sequence you ahve taken already with Calc I & II). Bottom line, it really does not matter the order in which you take them at this stage for your education. I would prefer Linear Algebra in the summer over Calc III though.

3

It really doesn’t matter in what order the courses are taken. I took differential equations and linear algebra in the same semester in between calc 2 and calc 3, and there were no issues with it. The three courses are pretty distinct from one another. There’s some overlap. In differential equations we did quite a bit with partial derivatives, which aren’t introduced until calc 3. However, the parts of partial derivatives needed for diff eq could be learned in about half of a lecture within the diff eq class, which is how we did it. The order in which you take them doesn’t really matter too much. I would advise against taking any, let alone two of these classes during the summer. The material has to be condensed into less time which means that things are going to be skipped or glossed over. It’ll be a really heavy workload.

If I had to pick one, I’d say differential equations will have more utility in your next couple of physics classes. I’d suggest taking that in the fall, and then calculus 3 in the spring, and you could take linear algebra concurrently with either one of them.

4

Multivariable calculus is likely to be helpful when your frosh-soph physics sequence covers electricity and magnetism.

5

I would also say Linear Algebra in the summer and Calc III in the fall. I waited to take linear algebra until after finishing Calc III, ODE, and PDE… So really it does not matter at what point you take it, though I would say the sooner the better.

In my experience, Calc III was probably the toughest math course so I wouldn’t suggest taking it in the summer, let alone alongside linear algebra. Besides, I took Calc III concurrently with Physics II (intro E&M) and they complemented each other very well, actually. You will do (very) basic line and surface integrals in your intro E&M class and so this provides some motivation for the things that you’ll learn in Calc III. That was such a fun semester for me.

I also took Differential Equations alongside Modern Physics and Optics (2 separate courses for me) in my sophomore year. The Optics course was actually an upper-level elective and we did use a bit of linear algebra when playing with Jones and Mueller polarization matrices. Also a bit of mathematical manipulation using Euler’s Theorem and complex exponentials, which you will run into in Differential Equations.

Don’t worry too much about the order in which you take these classes. Just try your best and have some fun!